coordine

Coordine is a theoretical framework for representing and manipulating coordinates across multiple reference frames within a unified algebraic structure. It extends conventional coordinate systems by treating frames as elements of a coordine manifold, enabling direct composition of inter-frame transformations and consistent handling of non-Euclidean geometries.

It introduces coordine operators, which generalize matrices and quaternions to encode rotation, translation, scaling, and more general diffeomorphisms in a single object. A coordine of a point is defined relative to a chosen base frame, and a coordine transform maps points and frames to an alternative base.

In theory, coordine can simplify complex pipelines in robotics, computer graphics, and GIS by reducing the number of intermediate representations required to move data between frames. It also provides a language for composing transformations with minimal risk of inconsistency, thanks to its algebraic rules.

Coordine was proposed in theoretical discussions as a conceptual tool for teaching and research. It has not been adopted as a standard in industry, and its practical implementations are limited to experimental or pedagogical settings.

Related topics include coordinate system, transformation matrix, Lie group, homogeneous coordinates, manifold, and non-Euclidean geometry.